Before placing an artificial implant into a human or animal body the implant must be sterilized. The material, furthermore, must not only be biocompatible, but have as long a life as is feasible after sterilization. The importance of this latter characteristic, i.e. useful life expectancy, is accentuated when the implant is a load-bearing one, such as a total joint arthroplasty (e.g. a hip or knee).
For many years, polyethylene, and in particular, ultra high molecular weight polyethylene (UHMWPE), has been used for this purpose. Sterilization is accomplished in at least one of several ways. One known way was to irradiate the implant (e.g. joint replacement) with a gamma ray dose of 2.5-4.0 Mrads in the presence of air. While highly effective as a sterilization technique, it was known to result, at times, in the formation of free radicals in the polyethylene which combined with oxygen to eventually degrade the polymer and thus reduce its effective useful life. Such degradation, it has been found, not only occurs during shelf storage but, unfortunately, can also continue to occur after implantation in the body.
As a result of this undesirable degradation, gamma sterilization in air is generally no longer used in most UHMWPE implant situations, and other alternatives have been devised. For example, low oxygen environment gamma irradiation, ethylene oxide, and gas plasma sterilization are currently more often used. Unfortunately, it is yet to be clearly ascertained to what extent these new sterilization methods either inhibit or cause mechanical degradation of the polyethylene during shelf storage and/or after implantation in the body.
There are two particular times at which the testing of an implant to determine its "degradation" characteristic (or susceptibility) normally occurs. The first, of course, is before implantation. The next is if the implant is removed for failure or is suspected of being near failure. Ascertaining the true cause of failure aids future improvements. Moreover, being able to predict in vivo wear behavior in advance would obviously materially aid the technology and patients, alike.
It was known prior to this invention that meaningful comparative mechanical behavior data could be obtained for analyzing polyethylene implants by deriving and comparing load vs. displacement curves using small sample punch test techniques on material of a known polyethylene "standard" (i.e. nondegraded) implant and on material of an implant suspected of having experienced degradation or being tested for use, failure, or potential degradation. While such techniques are very useful, they do not measure true stress and corresponding true strain which, if capable of measurement, would give a more accurate indication of levels of degradation due to the changes which a ductile polymeric material, such as UHMWPE, goes through during multiaxial (e.g. biaxial) deformation.
While various physical and chemical properties of polyethylene can be readily measured by well known techniques, it is only recently that techniques for performing measurements of mechanical behavior on localized sections of such a material have been developed. For example, uniaxial tensile testing of 200-400 .mu.m thick sections prepared from acetabular components have been utilized to investigate changes in mechanical behavior of the material in heavily oxidized subsurface regions, including local oxidation in total knee replacements. Yet another study prepared miniature tensile specimens from tibial components to compare mechanical properties of implants sterilized with ethylene oxide and gamma radiation. Unfortunately, the highly curved surfaces of total joint replacement components makes the fabrication of numerous long, flat uniaxial tensile specimens from a single implant technically impractical, and sometimes unfeasible.
Miniature specimen small punch testing techniques have heretofore been developed for measuring mechanical behavior of metals. Such known techniques have, in fact, been used successfully to characterize the true stress--true strain behavior, as well as the ductility and fracture resistance of metals. This development of the small punch test for metallic materials was driven by the need to measure in-service degradation of mechanical properties of metals with a limited volume of available material. The small specimen sizes (e.g. 0.02 inches thick) required for the test also provided a useful method for characterizing the material at specific locations in a component or a structure.
Certain researchers have heretofore empirically correlated the results of small punch mechanical behavior with conventional, relatively large test specimen mechanical behavior in metals. A major disadvantage of this empirical approach is the need to accumulate a large volume of mechanical (e.g. tensile and fracture) data for a given material in order to make reliable engineering predictions from small punch test results.
A known nonempirical alternative interpretation of the results of the small punch test data accumulated during the testing of metals is disclosed in U.S. Pat. No. 4,567,774. The technique reported uses the finite element method, or FEM, to infer conventional tensile stress-strain properties. Another known nonempirical technique matches the observed small punch load-displacement curve of the metal under analysis with a database of experimental and analytically simulated small punch load-displacement curves. From such a comparison, tensile stress-strain behavior in that metal can be inferred (i.e. an inferred true stress vs. true strain curve can be obtained). Such a stress/strain curve has been used to compute the local strain energy density accumulated to initiate cracking (i.e. fracture property) in the small punch metal specimen. Tensile and fracture properties using this known approach have been reasonably accurate for a wide range of metals. However, due to limitations in the constitute theory in these various nonempirical alternatives, they do not provide satisfactory results when applied to polymers such as polyethylene.
In this respect, the von Mises yielding criterion, which has been incorporated into the finite element models when nonempirical techniques have been employed, has been validated for metals. However, the theory has significant limitations with polymers generally, and with polyethylene specifically. For example, when applied to large-scale deformation mechanical behavior under multiaxial loading conditions when polymers stretch significantly, the von Mises yielding criterion no longer applies. Thus, these methods do not produce reliable estimates of the large-scale mechanical behavior of polymers under multiaxial loading conditions during the drawing (i.e. stretching) phase, which may often be of particular interest for the particular polymer under investigation. "Large-scale mechanical behavior" is defined (and known) as the behavior of a body under conditions wherein strains experienced are plastic over much of the body's volume (i.e. the "stretching" or "drawing" phase). In short, the known finite element based methods have not been found useful in reliably measuring or predicting stress/strain behavior for ductile polymers during the "stretching" phase. This is particularly true for polyethylene during the multiaxial loading conditions produced during and by a small punch test.
Despite the above drawbacks, the load-displacement behavior obtained by the known small punch testing methods for polymers, in general, and for polyethylene, in particular, has provided some useful results. In such tests, the punch head is caused to interact with the polymeric specimen at a constant displacement rate for the duration of the test. By gathering data and creating a "punch load vs. displacement curve" resulting from such a test on a particular material, the curve generated displays certain distinctive features, including an initial bending phase followed by a membrane drawing or stretching phase. In contrast, when metals are tested, virtually the entire test preceding the initiation of failure (cracking) consists of the bending phase with little or no stretching taking place. Thus, while load vs. displacement curves are highly useful for comparative analysis of metals, they are less satisfactory for use when comparing ductile polymers where failure initiates well after stretching has begun. In ductile polymers, their characteristics may differ markedly in the drawing phase, which characteristics are then not manifested in the load vs. displacement curves. Since in vivo implants may often be subjected, at least on their articulating surfaces, to multidirectional forces which create "drawing" or "stretching", it is important for a more accurate comparative analysis to generate curves which manifest the behavior of the polymer under "drawing" or "stretching" conditions. It has been left to this invention to achieve this more accurate result, as discussed below.
In this respect, and by way of a more detailed description, prior to our invention the mechanical behavior of polyethylene during the above-described small punch test has been empirically characterized from the load-displacement curve by measuring the initial peak load, the ultimate load, the ultimate displacement, and the work to failure (i.e., the area under the load-displacement curve). The small punch test has thus been used to characterize the load-displacement mechanical behavior of polyethylene with an uncertainty, in some instances, of less than 5%. Comparative analysis of a load-displacement curve obtained from a small punch test on a given material has then been compared with a curve similarly obtained for a known "standard" or "reference" material. Such a comparison has then been used to determine the acceptability of the material under test by subjectively comparing the shape of the load vs. displacement curve generated with that of the known "standard" material. Marked differences in the two curves resulted in rejection of the tested material. Absent from the comparison as stated above was a comparative analysis of the stress-strain behavior of either the "standard" material or the test material as it went through its stretching phase.
Despite the reproducibility and utility of such tests and of the load-displacement curves obtained, therefore, such results from this small punch testing are not completely satisfactory. For example, it has been observed that during the drawing phase of the test, a polyethylene specimen undergoes strain hardening or strain softening, depending upon the processing history and crosslink density of the polymer. Consequently, the load-displacement curves heretofore obtained do not permit a full analysis of the true stress-strain behavior of a ductile polymer, such as polyethylene, as would otherwise be desirable to know, particularly for assessing degradation or crosslinking in human implants.
It is thus apparent from the above that the prior art testing systems and procedures have not been able to fully characterize the large deformation mechanical behavior of ductile polymers in equibiaxial tension and, in this respect, have been unable to measure and generate complete true stress-true strain curves for comparative or other useful analytical purposes, particularly, but not necessarily limited to, ductile polymeric materials used in human (or animal) implants.
As used herein the term "true strain" (.epsilon.) is defined as: EQU .epsilon.=ln(t.sub.o /t) (1)
wherein t.sub.o is the initial thickness of the sample of the material being tested; t is the instantaneous thickness of the material at any point in time, and at the location where true strain is being measured during punch test deformation, including up to catastrophic failure; and in is the natural logarithm. PA1 wherein P is the applied load; R is the radius of the hemispherical punch head used in the punch test; and t is the thickness of the sample being tested at any instant in time, including up to catastrophic breakage (failure). In certain embodiments the factor .pi.t.sup.2 is so small compared to the factor 2.pi.Rt, as to be properly considered negligible and thus may be ignored (i.e. not calculated) without significant loss of accuracy. PA1 a) providing a ductile polymeric material specimen having a generally planar shape defining substantially parallel first and second spaced planar surfaces having an initial substantially uniform thickness (t.sub.o) therebetween; PA1 b) providing a punch system which includes a movable punch head comprised of a first substantially hemispherical end having a predetermined radius (R) and means for mounting the specimen in engagable alignment with the first end of the punch head; PA1 c) mounting the specimen in engagable alignment with the punch head; PA1 d) engaging a planar surface of the specimen with the first end of the punch head; PA1 e) substantially equibiaxially deforming the specimen with the punch head; PA1 f) determining the thickness of the specimen during the deformation of the specimen by the punch head; PA1 g) determining the load applied by the punch head during the deformation of the specimen; and PA1 h) determining the true stress and true strain of the specimen at at least one point in time during the deformation, according to the following formulae: ##EQU2## PA1 wherein P is the load applied; t.sub.o is the initial thickness of the specimen; t is the thickness of the specimen at the point in time of the determination during deformation; R is the radius of the punch head; and ln is the natural logarithm. PA1 a) means for calculating the true strain of the specimen during deformation using the thickness as measured according to the formula: EQU true strain=ln(t.sub.o /t) PA1 wherein t.sub.o is the initial thickness of the specimen; t is the measured thickness of the specimen; and ln is the natural logarithm; and PA1 b) means for controlling the relative movement between the punch head and the mounting means to achieve a constant strain rate during deformation in response to the calculation of the strain rate.
As further used herein, the term "true stress" (.sigma.) is defined as: ##EQU1##
By the use of these two formulae in combination with certain unique method steps and apparatus, true stress/strain data may now be readily generated for ductile polymeric materials throughout the deformation of the material up to failure, thereby generating data which better reflects the mechanical changes in such polymeric material which occur when the polymer is deformed. From such data then, more meaningful comparative analyses can be done, particularly with respect to analyzing useful life and failure mode characteristics in various pieces of equipment made of such materials including, of course, human and animal implants, and other known areas where shelf life, etc., are important factors to assess and/or to predict.
In this respect, it is to be understood that this invention's utility is not necessarily restricted to human or other animal implants, to polyethylene polymers, nor to assessing failures after the implants have been removed. To the contrary, it is envisioned by this invention that "in situ" sampling is and may become feasible in the future. Due to the relatively small size of the sample needed in the tests herein used, it is quite conceivable that a sample may be taken of a particular polymeric product while still in situ in its intended environment (e.g. while still implanted or, if an industrial product, while still located in the machine in which it is functioning). Moreover, as new polymers are developed or old ones find new uses, this invention will become equally applicable to them.
From the above, it is apparent that there exists a need in the art for a new technology which can measure true stress and true strain in a ductile polymeric material under deformation and from such measurements gather data which can be used to do numerous useful things including assessing for acceptability and/or cause of failure in sterilized polymeric implants. It is a purpose of this invention to fulfill this and other needs which will become more apparent to the skilled artisan once given the following disclosure.